Such a sealing arrangement and such a radial shaft seal ring are disclosed in European patent application EP 0 744 567 A1. The first sealing lip is configured as a dust lip and it has concentrically encircling sealing ribs, whereby the sealing ribs are perforated at circumferential places that are offset with respect to each other in the circumferential direction. Such a configuration vents the space between the two sealing lips. The space between the two sealing lips is configured as a lubricant reservoir and is filled with a lubricant in order to achieve improved emergency running properties. The sealing ribs of the sealing lips are configured in such a way that, in each case, a conveying effect is generated in the direction of each of the adjacent spaces that are to be sealed. For this purpose, the intersecting conical surfaces of the appertaining sealing ribs are configured to be essentially minor-image to an imaginary radial plane that runs through the lubricant reservoir.